Numerical Study of Turbulence Modeling for Analysis of Combustion Instabilities in Rocket Motor

로켓엔진의 연소 불안정 해석을 위한 난류 모델링의 수치적 연구

  • 임석규 (인하대학교 항공우주공학과 대학원) ;
  • 노태성 (인하대학교 항공우주공학과)
  • Published : 2002.06.01

Abstract

A numerical analysis of unsteady motion in solid rocket motors with a nozzle has been conducted. The numerical formulation including modified $\kappa$-$\varepsilon$ turbulence model treats the complete conservation equation for the gas phase and the one-dimensional equations in the radial direction for the condensed phase. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations. After obtaining a steady state solution, pulse and periodic oscillations of pressure are imposed at the head-end to simulate acoustic oscillations of a travelling-wave motion in the combustion chamber. Various steady and unsteady state features in the combustion chamber of a rocket motor has been analyzed as results of numerical calculations.

고체 추진 로켓 내부 연소실의 비정상 유동을 수치적으로 해석하였다. 완전 보존식을 이용하여 2 차원 축-대칭 연소실 안의 연소 불안정을 해석하기 위한 수치 기법을 구성하였는데 비정상 유동을 해석하기 위한 수정된 $\kappa$-$\varepsilon$ 난류 모델이 사용되었다. 이산화한 지배 방정식은 연관된 경계 조건을 포함하여 dual time-stepping 방법으로 시적분 하였다. 정상 상태의 계산을 기반으로 연소실 내의 천이 압력파의 비정상 상태를 수치적으로 모사하기 위하여 압력 펄스 및 압력 변동을 연소실 상단에 부과하였다. 로켓 모터 연소실 내의 다양한 정상 상태 및 비정상 상태의 특성을 계산 및 해석하였다.

Keywords

References

  1. Culick, F. E. C., 'Stability of Longitudinal Oscillations with Pressure and Velocity Coupling in a Solid Propellant Rocket,' Combustion Science and Technology, Vol.2, No.4, 1970, pp.179-201 https://doi.org/10.1080/00102207008952247
  2. Price, E. W., 'Velocity Coupling in Oscillatory Combustion of Solid Propellants,' AIAA Journal, Vol.17, 1979, pp.799-800 https://doi.org/10.2514/3.61229
  3. Flandro, G. A., 'Effect of Vorticity on Rocket Combustion Stability,' Jounal of Propulsion and Power, Vol. 11, No. 4, July 1995
  4. Roh, T. S., Tseng, I. S., and Yang, V., 'Effects of Acoustic Ocsillations on Flame Dynamics of Homogeneous Propellants in Rocket Motors,' Journal of Propulsion and Power, Vol. 11, No. 4 , July 1995
  5. Roh, T. S., Apte, S. V., and Yang, V., 'Transient Combustion Response of Homogeneous Solid Propellant to Acoustic Oscillations in a Rocket Motor,' Proceedings of Twenty-Seventh Symposium (International) on Combustion, Combustion Inst. Pittsburgh, PA, 1998, pp. 2335-2341
  6. King, M. K., 'Erosive Burning of Solid Propellants,' Journal of Propulsion and Power, Vol 9, No. 6, 1993
  7. Malhotra, S. and Culick, F. E. C., 'On the Pathways of Energy Transfer in Combustion Chambers,' AIAA Paper 2000-3288, July 2000
  8. Culick, F. E. C., 'Combustion Instabilities -Mating Dance of Chemical, Combustion, and Combustor Dynamics,' AIAA Paper 2000-3178, July 2000
  9. Mcbrid, B. J. and Gordon, S. and Reno, M. A. , 'Coefficient for Calculating Thermodynamic and Transport properties of Individual Species,' NASA TM-4513, 1993
  10. Reid, R. C., Prausnitz, J. M., and Poling, B. E., The Properties of Gases and Liquids, 4th ed., Mcgraw-Hill, New York, 1987, pp. 407-410
  11. Zenin, A. A., 'Structure of Temperature Distribution in Steady-State Burning of a Ballistite Powder,' Combustion, Explosion and Shock Waves, Vol. 2, No.2, 1966, pp. 67-76 https://doi.org/10.1007/BF00749238
  12. Rodi, W., 'Experience with Two-Layer Models Combining the k-$\varepsilon$ Model with a One-Equation Model near the wall,' AIAA Paper No. 91-0216, 1991
  13. Fan, S. and Lakshminaravana, B., 'Low-Reynolds-Number k-$\varepsilon$ Model for Unsteady Turbulent Boundary-Layer Flows.' AIAA Jounal, Vol. 31, No. 10, October 1993, pp. 1774-1784
  14. Tseng. I. S., and Yang. V., 'Combustion of a Double-Base Homogeneous Propellant in a Rocket Motor,' Combustion and Flame, Vol. 96, 1994, pp. 325-342 https://doi.org/10.1016/0010-2180(94)90102-3
  15. Yamadam K., Goto, M., and Ishikawa, N., 'Simulative Study on the Erosive Burning of Solid Rocket Motors,' AIAA Journal, Vol. 14, No. 9, 1976, pp. 1170-1176 https://doi.org/10.2514/3.61451
  16. Osborn, J. R. and Burick, R. J., 'Technique for the Measurement of the Erosive Burning Rate of Solid Rocket Propellants,' Second International Symposium on Nucleonics in Aerospace, July 1967, pp.87-94
  17. T'ien, J. S., 'Theoretical Analysis of Combustion Instability,' Fundamentals of Solid-Propellant Combustion, AIAA Progress in Astronautics and Aeronautics, Vol. 90, 1984, pp.791-840